Amgen Inc. is close to sewing up a deal to buy fellow biotechnology concern Onyx Pharmaceuticals Inc., in a takeover that could be valued at $10.5 billion, according to people familiar with the matter.

A deal between the companies is likely to be announced Monday, if not sooner, the people said Saturday. It would value Onyx at $125 a share in cash, the people said. One of them cautioned that the talks could still fall apart before...